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Eigenvalue problem of the Lame operator on a domain with a multi- structure

Research Project

Project/Area Number 22540216
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionHokkaido University

Principal Investigator

JIMBO Shuichi  北海道大学, 大学院・理学研究院, 教授 (80201565)

Co-Investigator(Kenkyū-buntansha) HONDA Naofumi  北海道大学, 大学院・理学研究院, 准教授 (00238817)
NAKAMURA Gen  北海道大学, 名誉教授 (50118535)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsラメ作用素 / 固有値問題 / 領域変形 / 複合構造 / 特異摂動問題 / 固有振動 / 弾性方程式 / 摂動公式 / ストークス作用素 / 固有値 / 特異的領域変形 / 漸近公式
Research Abstract

I studied the eigenvalu problem of the Lame operator, which is obtained from the oscillation property of elastic body. I dealt with the compex domain which is a union several thin regions. The limit system when the thinnes goes to zero, is a 4th order ODE system with a complicated compatibility condtions on the verticies. I also dealt with the eigenvalue problem of a certain Lame operator with the low stiffness coefficient. I obtained the limit system, which is related with the eigenvalue problem of the Stokes operator in a fluid dynamical problem with the Dirichlet condition or the slip boundary condition.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (36 results)

All 2013 2012 2011 2010

All Journal Article (11 results) (of which Peer Reviewed: 11 results) Presentation (24 results) (of which Invited: 3 results) Book (1 results)

  • [Journal Article] Hadamard variation for electromagnetic frequencies, Geometric Properties for Parabolic and Elliptic PDE's, R.Magnanini et al. (eds)2013

    • Author(s)
      S.Jimbo
    • Journal Title

      INdAM series

      Volume: 2 Pages: 179-200

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Multi-specialization and multi-expansions2013

    • Author(s)
      N.Honda
    • Journal Title

      Advances in Mathematics

      Volume: 232 Pages: 432-498

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hadamard variation for electromagnetic frequencies2013

    • Author(s)
      Shuichi JIMBO
    • Journal Title

      Geometric Properties for Parabolic and Elliptic PDE's, R.Magnanini et al. (eds)

      Volume: 2 Pages: 170-200

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multi-specialization and multi-asymptotic expansions2013

    • Author(s)
      Naofumi HONDA
    • Journal Title

      Advances in Mathematics

      Volume: 232 Pages: 432-498

    • NAID

      120006459687

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A non destructive method for damage detection in steel-concrete structures based on finite eigendata2012

    • Author(s)
      S.Jimbo, A.Morrasi, G.Nakamura,K.Shirota
    • Journal Title

      Inverse Problems in Science and Engineering

      Volume: 20 Pages: 233-270

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A non-destructive metnod for damage inspection in steel-concrete structures based on finite eigendata2012

    • Author(s)
      Jimbo, Morassi, Nakamura, Shirota
    • Journal Title

      Inverse problems in science and engineering

      Volume: 20 Pages: 233-270

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stratified Whitney jets and temperedul tradistributions on the subanaly ticsite2011

    • Author(s)
      N.Honda,G.Morando
    • Journal Title

      Bulletin di la Societe Mathematique de France

      Volume: 139 Pages: 389-435

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Geometric properties of the Riemann surface associated with Noumi - Yamada system with a large parameter2011

    • Author(s)
      T.Aoki, N.Honda
    • Journal Title

      J.Math. Soc. Japan

      Volume: 63 Pages: 1085-1119

    • NAID

      10030344748

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stratified Whitney jets and tempered ultradistributions on the subanalytic site2011

    • Author(s)
      Honda, Morando
    • Journal Title

      Bulletin de la Societe Mathematique de France

      Volume: 139 Pages: 389-435

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stratified Whitney jets and tempered ultradistributions on the subanalvtic site2011

    • Author(s)
      N.Honda, G.Morando
    • Journal Title

      Bulletin de la Societe Mathematique de France

      Volume: (印刷中)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Geometric properties of the Riemann surface associated with the Noumi-Yamada system with a large parameter2011

    • Author(s)
      T.Aoki, N.Honda
    • Journal Title

      Journal of Mathematical Society of Japan

      Volume: (印刷中)

    • NAID

      10030344748

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] 一数学者の出会った弾性方程式族の諸問題2013

    • Author(s)
      中村玄
    • Organizer
      北海道大学数学教室談話会
    • Place of Presentation
      北海道大学
    • Year and Date
      2013-02-07
    • Related Report
      2012 Final Research Report
  • [Presentation] Domain variation and electromagnetic frequencies2013

    • Author(s)
      S.Jimbo
    • Organizer
      14th North Eastern Symposium on Mathematical Analysis
    • Place of Presentation
      Tohoku University (Sendai)
    • Related Report
      2012 Final Research Report
  • [Presentation] Domain variation and electromagnetic frequencies2013

    • Author(s)
      Shuichi JIMBO
    • Organizer
      第14回北東数学解析研究会
    • Place of Presentation
      東北大学(仙台市)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 領域変形と楕円型作用素の固有値摂動問題2012

    • Author(s)
      神保秀一
    • Organizer
      偏微分方程式セミナー
    • Place of Presentation
      北海道大学
    • Year and Date
      2012-07-04
    • Related Report
      2012 Final Research Report
  • [Presentation] 薄い領域上のラプラシアンの固有値問題2012

    • Author(s)
      神保秀一
    • Organizer
      偏微分方程式セミナー
    • Place of Presentation
      北海道大学
    • Year and Date
      2012-05-07
    • Related Report
      2012 Final Research Report
  • [Presentation] 弾性体方程式に現れる固有値の特異摂動問題2012

    • Author(s)
      神保秀一
    • Organizer
      変分問題セミナー
    • Place of Presentation
      首都大学
    • Year and Date
      2012-03-16
    • Related Report
      2012 Final Research Report
  • [Presentation] Regulardomainvariationandelectromagneticfrequencies2012

    • Author(s)
      神保秀一
    • Organizer
      日本数学会関数方程式分科会一般講演
    • Place of Presentation
      九州大学(福岡市)
    • Related Report
      2012 Final Research Report
  • [Presentation] 弾性体方程式の固有値に関する特異摂動問題2012

    • Author(s)
      神保秀一
    • Organizer
      第8回非線形の諸問題
    • Place of Presentation
      宮崎県婦人会館(宮崎市)
    • Related Report
      2012 Final Research Report
  • [Presentation] Domain variation and electromagnetic frequencies2012

    • Author(s)
      S.Jimbo
    • Organizer
      Nonlinear Partial Differential Equations, Dynamical systems and their Application
    • Place of Presentation
      RIMS Kyoto University (Kyoto)
    • Related Report
      2012 Final Research Report
  • [Presentation] Domain variation for electromagnetic frequencies2012

    • Author(s)
      Shuichi JIMBO
    • Organizer
      Nonlinear partial differential equations, dynamical systems and their application
    • Place of Presentation
      京都大学数理解析研究所(京都市)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 弾性体方程式の固有値に関する特異摂動問題2012

    • Author(s)
      神保秀一
    • Organizer
      研究集会『第8回 非線型の諸問題』
    • Place of Presentation
      宮崎県婦人会館(宮崎市)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Regular domain variation and electromagnetic frequencies2012

    • Author(s)
      神保秀一
    • Organizer
      日本数学会関数方程式分科会
    • Place of Presentation
      九州大学(福岡市)
    • Related Report
      2012 Annual Research Report
  • [Presentation] Domain variation and Electromagnetic Frequencies2011

    • Author(s)
      Shuichi JIMBO
    • Organizer
      INdAM Workshop, Geometry of solutions to Parabolic and Ellitptic PDE's
    • Place of Presentation
      Parazzone (Italy)
    • Year and Date
      2011-06-24
    • Related Report
      2011 Annual Research Report
  • [Presentation] Eigenvalues of the Elliptic operator including a large nonlocal term2011

    • Author(s)
      S. Jimbo
    • Organizer
      Seoul Univ.-Hokkaido Univ. Joint seminar
    • Place of Presentation
      Seoul National University
    • Related Report
      2012 Final Research Report
  • [Presentation] Domain variation and electromagnetic frequencies2011

    • Author(s)
      S.Jimbo
    • Organizer
      INdAM workshop on Geometric properties for parabolic and elliptic PDE's
    • Place of Presentation
      Cortona, Italy
    • Related Report
      2012 Final Research Report
  • [Presentation] Singular perturbation of domains and electromaenetic oscillation2010

    • Author(s)
      神保秀一
    • Organizer
      洞爺湖解析セミナー
    • Place of Presentation
      洞爺湖 招待講演
    • Year and Date
      2010-09-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] 仮想変わり点の幾何とストークス係数2010

    • Author(s)
      本多尚文
    • Organizer
      日本数学会関数方程式分科会特別講演
    • Place of Presentation
      名古屋大学 招待講演
    • Year and Date
      2010-09-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] Virtual turning points and Stokes coefficients2010

    • Author(s)
      N.Honda
    • Organizer
      Recent developments in Resurgent Theory and Related Topics
    • Place of Presentation
      RIMS, Kyoto University (Kyoto)
    • Year and Date
      2010-06-28
    • Related Report
      2012 Final Research Report
  • [Presentation] Virtual turning points and Stokes coefficents2010

    • Author(s)
      N.Honda
    • Organizer
      Recent Developments in Resurgent Theory and Related topics, RIMS Symposium
    • Place of Presentation
      京大数理解析研 招待講演
    • Year and Date
      2010-06-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] Singular perturbation of domains and the characterization of the behavior of the eigenvalues of several elliptic operators2010

    • Author(s)
      Shuichi JIMBO
    • Organizer
      2010NCTS workshop on Calculus of Variation and Related Topics
    • Place of Presentation
      National Center for Theoretical Sciences, Tsing Hua, University, Beijing, China 招待講演
    • Year and Date
      2010-05-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] 領域変形とPDEs2010

    • Author(s)
      神保秀一
    • Organizer
      数理現象若手シンポジウム
    • Place of Presentation
      明治大学理工学部 招待講演
    • Year and Date
      2010-04-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] Domain variation andelectromagnetic oscillation2010

    • Author(s)
      神保秀一
    • Organizer
      洞爺湖解析セミナー
    • Place of Presentation
      洞爺山水ホテル和風(洞爺湖町)
    • Related Report
      2012 Final Research Report
  • [Presentation] 仮想変わり点の幾何とストークス係数2010

    • Author(s)
      本多尚文
    • Organizer
      日本数学会関数方程式分科会特別講演
    • Place of Presentation
      名古屋大学
    • Related Report
      2012 Final Research Report
  • [Presentation] Singular perturbation of domains and the characterization of the behavior of the eigenvalues in several elliptic operators2010

    • Author(s)
      S.Jimbo
    • Organizer
      2010 NCTS workshop on Calculus of Variation and related topics
    • Place of Presentation
      NCTS, National Tsinghua University, Taiwan
    • Related Report
      2012 Final Research Report
  • [Book] 位相空間2011

    • Author(s)
      神保秀一, 本多尚文
    • Total Pages
      230
    • Publisher
      数学書房
    • Related Report
      2011 Annual Research Report 2010 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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